User:Leigh.Samphier/Matroids/Axiom:Base Axiom (Matroid)/Formulation 6

Definition

Let $S$ be a finite set.

Let $\mathscr B$ be a non-empty set of subsets of $S$.

$\mathscr B$ is said to satisfy the base axioms if and only if:

\((\text B 6)\)

$:$

\(\ds \forall B_1, B_2 \in \mathscr B:\)

\(\ds x \in B_1 \setminus B_2 \implies \exists y \in B_2 \setminus B_1 : \paren {B_2 \cup \set x} \setminus \set y \in \mathscr B \)

See also

• User:Leigh.Samphier/Matroids/Equivalence of Definitions of Matroid Base Axioms